Defining parameters
Level: | \( N \) | \(=\) | \( 465 = 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 465.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(465, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 196 | 88 | 108 |
Cusp forms | 188 | 88 | 100 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(465, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
465.4.c.a | $38$ | $27.436$ | None | \(0\) | \(0\) | \(-6\) | \(0\) | ||
465.4.c.b | $50$ | $27.436$ | None | \(0\) | \(0\) | \(-6\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(465, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(465, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)